Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
906 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23773975 | C2 | semidirect |
| 2. #23773828 | C2 | semidirect |
| 3. #23763072 | C2 | semidirect |
| 4. #23763069 | C2 | semidirect |
| 5. #23763067 | C2 | semidirect |
| 6. #23763064 | C2 | semidirect |
| 7. C2×#19098284 | C2 | semidirect |
| 8. C79×#3147 | C2 | semidirect |
| 88. C2×C8×C79 | D8 | semidirect |
| 141. #3147 | D79 | semidirect |
| 147. C79 | #19616 | semidirect |
| 225. C2×C8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773975 | 2 |
| #23773828 | 2 |
| #23763072 | 2 |
| #23763069 | 2 |
| #23763067 | 2 |
| #23763064 | 2 |
| C2×#19098284 | 2 |
| C79×#3147 | 2 |
| #19616 | 79 |